Model Components

Each particle in a PFC model is denoted as a body to clarify the fact that it is not a point mass; a body is a discrete, rigid body with finite extent and a well-defined surface. The PFC model is populated with bodies, pieces, and contacts. There are three types of bodies: balls, clumps, and walls. Each body is composed of one or more pieces. A ball is {a unit-thickness disk in 2D; sphere in 3D}. A clump is a collection of pebbles that are {unit-thickness disks in 2D; spheres in 3D}. Clumps model arbitrarily shaped rigid bodies. The pebbles that make up a clump can overlap, but contacts do not exist between them; instead, contacts form between the pebbles and the pieces of other bodies. A wall is a collection of facets that are {linear segments in 2D; triangles in 3D}, and that form a manifold and orientable surface. Bodies may have surface properties that can be assigned to each piece on the body surface; these surface properties may be used to determine the piece interactions. Bodies exist within the model domain and cannot move outside of this region.

The motion of balls and clumps obeys Newton’s laws of motion, but the motion of walls is user-specified; thus, only balls and clumps have mass properties (mass, centroid position, and inertia tensor) and loading conditions (the force/moment applied from contacts, a body force arising from gravity, and an externally applied force/moment).

Contact mechanics is embodied in particle-interaction laws that employ a soft-contact approach, for which all deformation occurs at the contacts between the rigid bodies. The mechanical interaction between the surfaces of two bodies occurs at one or more pair-wise mechanical contacts. Contacts are created and deleted during the contact detection step of the cycle sequence based on piece proximity. A contact provides an interface between two pieces [1]. The interface consists of a contact plane with location \((\mathbf{x_c})\), a normal direction \((\hat{\mathbf{n}}_\mathbf{c})\) and coordinate system \((nst)\). The contact plane is centered within the interaction volume (either gap or overlap) of the two pieces, oriented tangential to the two pieces and rotated to ensure that relative motion of the piece surfaces remains symmetric w.r.t. the contact plane. Each contact stores a force \((\mathbf{F_c})\) and moment \((\mathbf{M_c})\) that act at the contact location in an equal and opposite sense on the two bodies [2]. The internal forces/moments are updated by the particle-interaction law. The interaction law utilizes the positions and relative motion of the two pieces to update the forces/moments. We refer to the particle-interaction law as a contact model. The surface properties may also be used as input [3].

Figure 1: Sketch of a PFC model showing bodies, pieces, and contacts (left) and the contact plane with the internal force (right).

A PFC model is created and manipulated by eliciting commands. The commands pertinent to each PFC model component are detailed in the section describing this component (i.e., among the sections “Balls,” “Clumps,” “Walls,” and “Contacts and Contact Models”). Many additional utilities exist to facilitate the modeling process; these are described in the “Common Model Objects” section. The listing of all commands related to PFC model components is available in the “PFC Command Summary” section, and a complete listing of all all commands available in PFC can be found in the “Command Summary” section.

Nearly all aspects of a PFC model are accessible via an internal scripting language called FISH. See the “FISH Scripting” section for an introduction to FISH. Similar to commands, the FISH functions available to access/modify PFC model components are detailed in the corresponding section describing this component. A listing of all FISH functions related to PFC model components can be found in the “PFC FISH Index” section, while the complete listing of all FISH functions available in PFC is provided in the “FISH Reference Summary” section, as well.

– Next Section: Cycling –

Endnotes

[1]

Contacts are referred to by the types of the two pieces. For example, a contact between a ball and facet is called a ball-facet contact and has a contact type of ball-facet. In the current PFC model, facet-facet contacts are not allowed and piece one is a ball or pebble while piece two is a ball, pebble, or facet to give five unique contact types: ball-ball, ball-pebble, ball-facet, pebble-pebble, and pebble-facet.

[2]	Contact models that simulate interaction at a distance update the force and two moments that need not be equal and opposite.

[3]	The contact model properties may be specified directly via Contact Model Assignment Table (CMAT). Additionally, the concept of inheritance can be used to specify whether or not piece properties are used to override the default contact model properties.